A DT sequence $y[n]$ is constructed from another DT sequence $x[n]$ according to the formula $y[n]=x[nN]$, where $N$ is a constant positive integer greater than one. (This process is usually called decimation, although this name would strictly be appropriate only if $N = 10$.)
a) Sketch a typical $x[n]$ and the corresponding $y[n]$ for, say, $N=3$.
b) Suggest a set of conditions to be imposed on the DTFT of $x[n]$ such that it will be possible to reconstruct $x[n]$ for all $n$ from $y[n]$ .
c) Describe a specific scheme for carrying out the reconstruction if the conditions of (b) apply.
d) The conditions on $x[n]$ that are sufficient to permit reconstruction of $x[n]$ for all $n$ given $y[n]$ are not unique. Describe at least one set of conditions different from those in (b) that will also suffice .
Thank you
